Disturbance in weak measurements and the difference between quantum and classical weak values

摘要

The role of measurement induced disturbance in weak measurements is ofcentral importance for the interpretation of the weak value. Uncontrolleddisturbance can interfere with the postselection process and make the weakvalue dependent on the details of the measurement process. Here we develop theconcept of a generalized weak measurement for classical and quantum mechanics.The two cases appear remarkably similar, but we point out some importantdifferences. A priori it is not clear what the correct notion of disturbanceshould be in the context of weak measurements. We consider three differentnotions and get three different results: (1) For a `strong' definition ofdisturbance, we find that weak measurements are disturbing. (2) For a weakerdefinition we find that a general class of weak measurements arenon-disturbing, but that one gets weak values which depend on the measurementprocess. (3) Finally, with respect to an operational definition of the `degreeof disturbance', we find that the AAV weak measurements are the leastdisturbing, but that the disturbance is always non-zero.